Processing math: 100%

SyzygyData

Current Betti Table Entry:

n=2

d=2

b=1

p=1

q=0

0 1 2 3
0 3 8 6 ·
1 · · · 1
2 · · · ·
0 1 2 3
0 (1,0,0) (2,1,0) (3,1,1) ·
1 · · · (3,3,3)
2 · · · ·
0 1 2 3
0 1 1 1 ·
1 · · · 1
2 · · · ·
0 1 2 3
0 1 1 1 ·
1 · · · 1
2 · · · ·

Below is a plot displaying the Schur decomposition. In the λ=(λ0,λ1) spot we place β1,λ(2,1;2), the multiplicity of Sλ occuring in the decomposition of K1,0(2,1;2). Here λ is the weight (λ0,λ1,λ2) where λ2 is determined by the fact that |λ| equals d(p+q)+b. The dominant weights are displayed in green. Click on an entry for more info!

1 2 3
0 · · ·
1 · 1 ·
2 · · ·

Below is a plot displaying the multigraded Betti numbers. In the (a0,a1) spot we place β1,a(2,1;2). Here a is the weight (a0,a1,a2) where a2 is determined by the fact that |a| equals d(p+q)+b. Entries with error corrected via our Schur decomposition algorithm are in orange. Click on an entry for more info!

0 1 2 3
0 · 1 1 ·
1 1 2 1 ·
2 1 1 · ·
3 · · · ·